Displaying similar documents to “Compatibility relations on codes and free monoids”

We introduce doubly-ranked (DR) monoids in order to study picture
codes. We show that a DR-monoid is free iff it is pictorially
stable. This allows us to associate with a set of pictures a
picture code which is the basis of the least DR-monoid
including .
A weak version of the defect theorem for pictures is established.
A characterization of picture codes through picture series is
also given.

We first prove an extremal property
of the infinite Fibonacci
word : the family of the palindromic prefixes
{} of
is not only a circular code but “almost” a comma-free one
(see Prop. 12 in Sect. 4).
We also extend to a more general situation
the notion of a necklace introduced
for the study of trinucleotides codes on the genetic alphabet,
and we present a hierarchy
relating two important classes of codes,
the comma-free codes and the circular ones.

This paper is the first step in the solution of the problem of finite completion of comma-free codes. We show that every finite comma-free code is included in a finite comma-free code of particular kind, which we called, for lack of a better term, canonical comma-free code. Certainly, finite maximal comma-free codes are always canonical. The final step of the solution which consists in proving further that every canonical comma-free code is completed to a finite maximal comma-free code,...